If p1⁢p2⁢⋯⁢pmsubscriptp1subscriptp2normal-⋯subscriptpmp_{1}p_{2}\cdots p_{m} and q1⁢q2⁢⋯⁢qnsubscriptq1subscriptq2normal-⋯subscriptqnq_{1}q_{2}\cdots q_{n} are two factorizations of the same element aaa into irreducibles, then m=nmnm=n.